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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Quasilinear elliptic equations via perturbation method


Authors: Xiang-Qing Liu, Jia-Quan Liu and Zhi-Qiang Wang
Journal: Proc. Amer. Math. Soc. 141 (2013), 253-263
MSC (2010): Primary 35B05, 35B45
Published electronically: May 9, 2012
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Abstract: We present a new approach to studying a class of quasilinear problems including the so-called Modified Nonlinear Schrödinger Equations (MNLS). We show that solutions of quasilinear equations can be obtained as limits of $ 4$-Laplacian perturbations.


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Additional Information

Xiang-Qing Liu
Affiliation: Department of Mathematics, Yunnan Normal University, Kunming, 650092, People’s Republic of China
Email: lxq8u8@163.com

Jia-Quan Liu
Affiliation: Department of Mathematics, Peking University, Beijing, 100871, People’s Republic of China
Email: jiaquan@math.pku.edu.cn

Zhi-Qiang Wang
Affiliation: Chern Institute of Mathematics, Nankai University, Tianjin, 300071, People’s Republic of China — and — Department of Mathematics and Statistics, Utah State University, Logan, Utah 84322
Email: zhi-qiang.wang@usu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11293-6
PII: S 0002-9939(2012)11293-6
Received by editor(s): January 26, 2011
Received by editor(s) in revised form: January 27, 2011, May 29, 2011, May 30, 2011, and June 9, 2011
Published electronically: May 9, 2012
Communicated by: Yingfei Yi
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.